Quadrupolar nuclei NMR using residual dipolar splittings in solids

ABSTRACT

A method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin l&gt;½ using magic angle spinning (=MAS) in solid powders and transfer of coherences from a neighboring nucleus with spin S= 1/2  to single- or double-quantum transitions of quadrupolar nuclei having spin l&gt;½, is characterized in that the transfer of coherences occurs through a combination of scalar and residual dipolar splittings. With the inventive method improved NMR-spectra can be obtained from which parameters can be extracted, which can be related to the structure and internal dynamics of solids containing the quadrupolar nuclei.

This application claims Paris Convention priority of EP 05 015 334.5 filed Jul. 14, 2005 the entire disclosure of which is hereby incorporated by reference

BACKGROUND OF THE INVENTION

The invention concerns a method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin l>½ using magic angle spinning (=MAS) in solid powders and transfer of coherences from a neighboring nucleus with spin S=½ to single- or double-quantum transitions of quadrupolar nuclei having spin l>½.

A method for obtaining NMR (=nuclear magnetic resonance) spectra of quadrupolar nuclei having spin l>½ is known from [32]-[36].

Although nitrogen is of universal importance in virtually all branches of biology, chemistry, and material science, and although nitrogen-14 is a very abundant isotope (99.4%), nitrogen-14 NMR has enjoyed relatively little popularity so far. In liquids, nitrogen-14 line-widths are very broad because of rapid quadrupolar relaxation, except in rapidly-tumbling molecules or in highly symmetrical environments such in tetraalkyl ammonium ions.^([1]) In solids, nitrogen-14 quadrupole interactions can be characterized in the absence of external magnetic fields by nuclear quadrupole resonance (NQR).^([2, 3]) In a static magnetic field, the strong quadrupole interaction between the nuclear quadrupole moment of a spin l=1 and the electric field gradient (EFG) at the site of the nucleus leads to very broad spectra (up to a few MHz) that are difficult to excite and observe.^([4-8]) The interaction of a nucleus with a quadrupole moment Q with the electric field gradient V at the site of the nucleus can be characterized by the quadrupole coupling constant C_(Q)=eQV_(ZZ)h and the asymmetry parameter η_(Q)=(V_(XX)−V_(YY))/V_(ZZ), where the principal components of the electric field gradient tensor are ordered V_(ZZ)>V_(XX)>V_(YY). The asymmetry parameters η_(Q) can cover the full range 0<η_(Q)<1.

Early examples of direct detection of ¹⁴N NMR used single crystals,^([4-8]) where one obtains a doublet for each ¹⁴N site, with reasonably narrow spectral lines (on the order of 1.5 kHz for C_(Q)≈3-4 MHz), provided that there are no significant crystal imperfections. The signals are spread over spectral ranges of several MHz, requiring very broad band-widths (or re-tuning of the circuits) for both excitation and signal acquisition. In static polycrystalline powders, the ¹⁴N signal intensity is spread over many MHz, so that it is difficult to recognize the singularities of the powder patterns. When the powders are spun at the magic angle, one observes families of spinning sidebands. Although for moderate spinning frequencies the signal intensity can be spread over hundreds of sidebands, quadrupole couplings up to C_(Q)=1.5 MHz have been observed by direct ¹⁴N MAS.^([9-13]) Not surprisingly, the envelopes of the spinning sidebands depend not only on the accurate adjustment of the magic angle, but also on the amplitude of the ¹⁴N radio-frequency pulses and on the bandwidth of the probe and receiver systems.

The frequencies of double-quantum transitions between the |m=+1> and |m=−1> levels in I=1 systems are not affected by first-order quadrupolar interactions, as shown for ²H NMR by Pines and co-workers.^([14]) In combination with cross-polarization between ¹⁴N (I=1) and suitable S nuclei, one can excite ¹⁴N double-quantum coherences.^([15-17]) By transferring coherence back and forth between ¹⁴N double-quantum coherences and S nuclei, one can achieve indirect detection.

The ¹⁴N double-quantum transitions can also be detected directly by overtone spectroscopy, ^([18-22]) where a radio-frequency field centered at twice the ¹⁴N Larmor frequency. This exploits the fact that double-quantum transitions are weakly allowed. Second-order quadrupole couplings, as shown in single crystals and powders, determine the line-shapes in overtone spectra.^([18-22]) Compounds with several ¹⁴N sites may lead to overlapping overtone patterns, which can in principle be separated by combining overtone spectroscopy with dynamic-angle spinning or with double sample rotation.^([23-27])

It is possible to achieve indirect detection of ¹⁴N in spinning samples by recoupling heteronuclear dipolar interactions with a suitable spin S such as ¹³C.^([28-30]) By applying pulses at ω₀ ^(N) in synchronism with sample rotation, one can interfere with the averaging of heteronuclear dipolar interactions. This leads to a dephasing of the signals of the S nuclei, thus providing information on the strength of the dipolar interaction. Recoupling can also be achieved by ¹⁴N irradiation near the overtone frequency.^([31, 32]) By stepping the RF frequency in the vicinity of ω₀ ^(N) or 2ω₀ ^(N), one obtains line shapes determined by first- or second-order quadrupole interactions respectively.^([31]) This may be regarded as continuous-wave approach to indirect detection of ¹⁴N spectra.

Another class of experiments exploits residual dipolar splitting (RDS), also known as second-order quadrupole-dipole cross term, between ¹⁴N (I=1) and S=½ nuclei such as ¹³C. ^([32-36]) Since the IS dipolar interactions are not averaged out completely by magic angle spinning, because the large quadrupole coupling of the I nucleus prevents its quantization along the direction of the static field, the S resonances are split into 1:2 doublets (each component featuring a narrow powder pattern) with a splitting D, which depends on the orientation of the C-N bond with respect to the quadrupole tensor. The largest peak corresponds to the superposition of the |m=+1> and |m=−1> states of the S=1 spin, while the smaller peak corresponds to the |m=0> state. The former is further split into a doublet 2J due to the heteronuclear J coupling. Inhomogeneous broadening or relaxation may of course mask these splittings. Residual dipolar splittings have been used by Clare et al.,^([29]) who stepped an RF field in the vicinity of ω₀ ^(N) while observing two-dimensional exchange spectra of the S (¹³C) nuclei. If the RF field is applied for a duration comparable to the rotor period, the populations of the ¹⁴N levels are partly interchanged. As a result, the two components of the doublet in the S (¹³C) spectrum are swapped.^([29])

It is the object of the invention to present a method for obtaining NMR spectra of quadrupolar nuclei having spin l>½ which overcomes the above mentioned problems.

SUMMARY OF THE INVENTION

This object is achieved, according to the invention, by a method mentioned above, characterized in that the transfer of coherences occurs through a combination of scalar and residual dipolar splittings. The inventive method enables one to achieve NMR-spectra that reveal patterns of quadrupolar couplings of the quadrupolar nuclei with extremely narrow line widths. Therefore improved NMR-spectra can be obtained from which parameters can be extracted, which can be related to the structure and internal dynamics of solids containing the quadrupolar nuclei.

The quadrupolar nuclei having spin l>½ are preferably chosen from the group ¹⁴N, ¹⁷O, ³⁵Cl, ³⁷Cl. Because of its great importance in biology, chemistry and material science ¹⁴N is highly preferred.

In a highly preferred variant the inventive method includes the following steps:

-   -   (i) excitation of the neighboring nucleus single quantum         coherence by cross polarization from protons,     -   (ii) applying a delay of T_(exc)≈½D, where D is the splitting         due to a combination of scalar and residual dipolar splittings,     -   (iii) applying an RF-pulse of duration τ_(P) to the quadrupolar         nuclei having spin l>½,     -   (iv) applying a π-RF-pulse to the neighboring nucleus in the         middle of an evolution interval t₁,     -   (v) applying an RF-pulse at t₁ of duration τ_(P) to the         quadrupolar nuclei having spin l>½, and     -   (vi) recording the signal of the neighboring nucleus with spin         S=½ after a duration τ_(rec)≈½D.

The neighboring nucleus with spin S=½ is preferably chosen from the group ¹³C, ³¹P, ¹⁵N, ²⁹Si, ¹H.

Advantageously the steps (i) to (vi) are repeated for N rotor-synchronized increments t₁=nΔt₁ with Δt₁=1/v_(rot) and n=1, 2,3 . . . N in the manner of 2-dimensional spectroscopy.

In a preferred variant the time domain signals S(t₁, t₂) are Fourier transformed with respect to t₁ to yield a spectrum of the quadrupolar nuclei having spin l>½ in the ω₁ domain and with respect to t₂ to yield a spectrum of the neighboring nucleus with S=½ in the ω₂ domain.

A variant of the NMR method according to the invention is characterized in that (π/2)_(φ) pulses are applied to the neighboring nucleus with S=½ at the beginning and at the end of an evolution interval t₁. Therewith the heteronuclear coherences can be converted into coherences of the I=½ nucleus .

Also in accordance with the invention is a variant of the method wherein a z-filter is used before the detection period. The excitation and reconversion are then symmetrical in time domain, which improves the spectra.

Further it is preferred, that from the obtained NMR spectra the quadrupolar coupling constant C_(Q), the asymmetry parameter η_(Q) of the quadrupolar nuclei having spin l>½ and the relative orientation of the quadrupolar tensor with respect to the bond between the quadrupolar nuclei having spin l>½ and the neighboring nucleus with S=½ are extracted.

It is shown that nuclear magnetic resonance (NMR) spectra of nitrogen-14 (spin l=1, with quadrupole couplings up to a few MHz) can be obtained by indirect detection in powders spinning at the magic angle (MAS). The method relies on the transfer of coherence from a neighboring nucleus with S=½ such as carbon-13 to single- or double-quantum transitions of nitrogen-14 nuclei. The transfer of coherence occurs through a combination of scalar and residual dipolar splittings, the latter being also known as second-order quadrupole-dipole cross terms. The two-dimensional (2D) NMR spectra reveal powder patterns determined by second-order quadrupolar couplings of nitrogen-14, which have line-widths that are about three orders of magnitude narrower than the first-order quadrupolar interaction. Analysis of the spectra yields the quadrupolar coupling constant C_(Q) and asymmetry parameter η_(Q) of nitrogen-14 and the relative orientation of the quadrupolar tensor with respect to the bond between the nitrogen-14 and S nuclei. These parameters, which can be subject to motional averaging, can be related to the structure and internal dynamics of nitrogen-containing solids.

Further advantages can be extracted from the description and the enclosed drawing. The features mentioned above and below can be used in accordance with the invention either individually or collectively in any combination. The embodiments mentioned are not to be understood as exhaustive enumeration but rather have exemplary character for the description of the invention.

The invention is shown in the drawings.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows a pulse sequence and coherence transfer pathways for the excitation of ¹⁴N single- or double-quantum coherences according to the invention;

FIG. 2 shows simulations of ¹⁴N single-quantum (SQ) powder patterns that result from the pulse sequence of FIG. 1 for different excitation intervals and ¹⁴N pulse lengths;

FIG. 3 shows simulations of ¹⁴N double-quantum (DQ) powder patterns with the same parameters as in FIG. 2;

FIG. 4 a shows an experimental ¹³C CPMAS in L-alanine;

FIG. 4 b shows an experimental ¹³C CPMAS in glycine;

FIG. 4 c shows a 2-dimensional ¹⁴N/¹³C correlation spectrum in L-alanine with single-quantum signals;

FIG. 4 d shows a 2-dimensional ¹⁴N/¹³C correlation spectrum in glycine with single-quantum signals;

FIG. 4 e shows a 2-dimensional ¹⁴N/¹³C correlation spectrum in L-alanine with double-quantum signals

FIG. 4 f shows a 2-dimensional ¹⁴N/¹³C correlation spectrum in glycine with double-quantum signals

FIG. 4 g-j shows projections of the ¹⁴N single- and double-quantum coherences of FIG. 4 c-f onto the δ₁ axis;

FIG. 5 a shows an experimental ¹³C CPMAS of L-leucine;

FIG. 5 b shows a two-dimensional ¹⁴N/¹³C correlation spectra obtained with single-quantum methods of L-leucine;

FIG. 5 c shows a two-dimensional ¹⁴N/¹³C correlation spectra obtained with double-quantum methods of L-leucine;

FIG. 6 a shows an experimental ¹³C CPMAS for the tripeptide L-ala-L-ala-gly;

FIG. 6 b shows a two-dimensional ¹⁴N/¹³C correlation spectra obtained with single-quantum methods for the tripeptide L-ala-L-ala-gly;

FIG. 6 c shows a two-dimensional ¹⁴N/¹³C correlation spectra obtained with double-quantum methods for the tripeptide L-ala-L-ala-gly;

FIG. 7 shows simulations of single-quantum and double-quantum ¹⁴N spectra; and

FIG. 8 shows simulations of single-quantum and double-quantum ¹⁴N spectra at different polar angles.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The method presented in this work exploits residual dipolar splittings between ¹⁴N (I=1) and a “spy” nucleus with S=½ such as ¹³C, in combination with scalar J couplings. The residual splitting D(¹⁴N, ¹³C), which decreases in inverse proportion to the static field strength B₀, is on the order of D≈30 Hz for ¹⁴NH₃ ⁺¹³C^(α)HRCOO⁻ in zwitterionic amino acids at B₀=9.4 T (400 MHz for protons), while J(¹⁴N, ¹³C) couplings in L-alanine are about 3.1 and 4.0 Hz for ¹⁴NH₃ ⁺R and ¹⁴NH₂R respectively, and around 8 Hz in peptide bonds.^([37]) If the magic angle is adjusted very accurately,^([38]) and if proton decoupling is optimized,^([39, 40]) the ¹³C^(α) lines of amino acids can be as narrow as 18 Hz, so that the residual dipolar splitting can readily be observed.^([38]) Even when the splittings are masked by inhomogeneous broadening, due to slight errors in the adjustment of the magic angle, temperature gradients, or magnetic susceptibility effects, the residual dipolar splittings can still be exploited, provided that they are larger than the homogeneous (‘refocusable’) line-width 1/(πT₂′). In amino acids, the time constant T₂′(¹³C^(α)) of spin-echo decays can be as long as 50 ms, so that 1/(πT₂′)=6 Hz is not exceptional for ¹³C^(α).

The pulse sequence and coherence transfer pathways for the novel two-dimensional correlation NMR methods are illustrated in FIG. 1. After exciting carbon-13 single-quantum coherence C_(x)=(T^(C) ₁₁+T^(C) ¹⁻¹)/2 in the usual manner by cross-polarization from protons, a delay τ≈½D leads to a state that can be described by a product of irreducible tensor operators T^(C) ₁₁T^(N) ₂₀. This state can also be represented by a product of Cartesian operators C_(x)(N_(z) ²−2E_(N)/3), where the unity operator E_(N) ensures that the product operator is traceless and orthonormal. For simplicity, we can loosely speak of a doubly-antiphase operator C_(x)N_(z) ². However, it turns out that irreducible tensor operators are more convenient to describe heteronuclear multiple-quantum coherences. A radio-frequency pulse applied in the center of the ¹⁴N spectrum can lead to a partial conversion into T^(C) ₁₁T^(N) _(1±1) and T^(C) ₁₁T^(N) _(2±1) (corresponding to ¹⁴N single-quantum coherences) or into T^(C) ₁₁T^(N) _(2±2), corresponding to ¹⁴N double-quantum coherences. Henceforth, we shall speak of nitrogen-14 single-uantum (SQ) or double-quantum (DQ) spectroscopy, which are distinct in their coherence transfer pathways (FIG. 1), and of course in the appearance of the spectra. In either case, a π pulse applied to ¹³C in the middle of the evolution interval t₁ not only interconverts T^(C) ₁₊₁ and T^(C) ¹⁻¹ to refocus the carbon chemical shifts, but also eliminates the effects of inhomogeneous decay, so that the attenuation of the signal by irreversible dephasing of the carbon-13 coherences is determined by the factor exp{-(τ_(exc)+t₁+τ_(rec))/T₂′(C)}. Terms containing T^(C) ¹⁻¹ are converted into T^(C) ₁₊₁ by the π pulse at t₁/2 and therefore cannot contribute to any observable pathways, unless a z-filter is inserted prior to signal observation. Note that in the fixed intervals τ_(exc) and τ_(rec), the inhomogeneous decay with a time constant T₂*<<T₂′ does not contribute to signal losses.

The heteronuclear coherences T^(C) ₁₁T^(N) _(1±1) and T^(C) ₁₁T^(N) _(2±1) or T^(C) ₁₁T^(N) _(2±2) are allowed to evolve freely during the evolution interval t₁ prior to symmetrical reconversion into observable single quantum coherence T^(C) ¹⁻¹. The experiment is repeated for N rotor-synchronized increments t₁=nΔt₁ with Δt₁=1/ν_(rot) and n=1, 2, 3, . . . , N, in the manner of two-dimensional spectroscopy. The time-domain signals S(t₁,t₂) are Fourier transformed with respect to t₁ to yield a ¹⁴N spectrum in the ω₁ domain, and with respect to t₂ to produce a ¹³C spectrum in the ω₂ domain. The coherence transfer pathways in FIG. 1 show that both single- and double quantum experiments lead to pure two-dimensional absorption line shapes since they retain two mirror-image pathways with respect to the ¹⁴N coherence order ρ_(N). Note that, in contrast to most other 2D experiments, the t₁ period is defined as the interval between the centers of the two ¹⁴N pulses, rather than as a period of free precession. Its initial duration corresponds to one rotor period, so that a first-order phase correction must be applied to the ω₁ domain. The initial free evolution interval between the pulses is 1/ν_(rot)−τ_(p).

The nitrogen-14 single- and double-quantum coherences evolve in the t₁ interval under the effect of the quadrupolar interaction and the chemical shift. The single-quantum coherences are affected by both first- and second-order quadrupole interactions, while the double-quantum coherences are affected only by second-order quadrupole effects. Synchronization of the increments Δt₁ with the spinner period 1/ν_(rot) leads to aliasing in the ω₁ domain, so that the spinning sidebands coincide with the center bands. The spinning sidebands can be observed separately if smaller time increments are chosen.

Many variants of the experiments can be conceived. For example, optional (π/2)_(φ) pulses applied to ¹³C at the beginning and at the end of the evolution period can convert T^(S) ₁₁T^(I) ₂₂ into T^(S) ₁₀T^(I) ₂₂ and back. Complementary experiments with different phases φ of the ¹³C pulse can be used. This variant allows one to avoid the T₂-decay of the T^(S) ₁₁ term in the t₁ interval. Another variant uses a z-filter before the detection period so that the excitation and reconversion are symmetrical even when there is a distribution of residual dipolar splittings. This improves the spectra if τ_(rec)<½D, so that the reconversion into in-phase C_(x) coherence is not complete.

FIG. 2 and FIG. 3 show simulations of SQ and DQ powder patterns as a function of the excitation and reconversion intervals τ_(exc)=τ_(rec) and of the ¹⁴N pulse length τ_(p). The thick lines show the spectra expected for ideal single- and double-quantum excitation. For quadrupole parameters that are typical for amino acids, the optimum τ_(p) for SQ excitation is about half as for DQ excitation.

In the experimental SQ and DQ spectra of FIG. 4, the ¹⁴N patterns have line-widths on the order of a few kHz, determined by the anisotropy of the second order quadrupole interaction. The SQ spectra are about twice as narrow at the DQ spectra. For L-alanine in FIG. 4 a, the residual dipolar splitting D(¹⁴N, ¹³C) is barely resolved at 9.4 T. The fact that ¹⁴N coherences can be excited efficiently even in the absence of a resolved residual dipolar splitting is demonstrated in FIG. 4 b for glycine.

FIG. 5 shows how the two crystallographic ally inequivalent ¹³C sites I and II in powdered L-leucine correlate with non-degenerate ¹⁴N quadrupole parameters estimated to C_(Q) ^(I)=1.2 MHz, η_(Q) ^(I)=0.3, C_(Q) ^(II)=1.1 MHz, η_(Q) ^(II)=0.1. Again, the SQ spectra are about twice as narrow at the DQ spectra.

FIG. 6 shows a challenging example of a tripeptide L-ala-L-ala-gly. The terminal ¹⁴NH₃ ⁺ group (site II) has similar parameters as in FIG. 4, except that is this case the SQ spectrum is broader than the DQ spectrum, which indicates motional broadening.^([41]) On the other hand, the amide groups —CO^(14 NH) ¹³C^(α)— have quadrupole parameters C_(Q) ^(I) and C_(Q) ^(III) of at least 3 MHz. It is remarkable that signals could be excited and observed with a ¹⁴N RF strength of only 60 kHz for such large quadrupole interactions.

The sensitivity is largely determined by the quantum yield of two-way coherence transfer. The efficiency of the conversion of T^(C) ₁₁T^(N) ₂₀ into T^(C) ₁₁T^(N) _(2±1) or T^(C) ₁₁T^(N) _(2±2) and back under MAS is determined by the amplitude ω₁ ^(N) N and duration τ_(p) of the ¹⁴N pulse. Numerical calculations (neglecting relaxation) with integration over all crystallite orientations show that with C_(Q)=1.2 MHz, η_(Q)=0, ν_(RF) ^(N)=60 kHz, τ_(p)=15 μs, D=30 Hz, and τ_(exc)=τ_(rec)=15 ms, the efficiency of the two-way coherence transfer to SQ or DQ and back is about 5%. Experiments indicate an efficiency of 2% for SQ or DQ spectra for the first t₁ increment, compared with a simple ¹³C CPMAS spectrum.

The experiments work in principle with ¹³C in natural abundance. The sensitivity can be boosted by a factor of about 100 by ¹³C enrichment, as we have done to optimize the experimental conditions. In principle, the experiment can work with any S=½ “spy” nucleus such as phosphorus-31, nitrogen-15, silicon-29, etc., provided that there is a non-vanishing residual dipolar splitting and/or scalar coupling between the spy nucleus and ¹⁴N. In some cases, the J coupling may be larger than D. Even protons could be used as spy nuclei, provided the broadening due to homonuclear dipolar proton-proton couplings does not mask the residual dipolar splittings. It is possible to contemplate the indirect detection of other quadrupolar nuclei with S=3/2, 5/2 etc., such as ³⁵Cl, ¹⁷O, etc., provided that one can exploit a residual dipolar splitting with suitable spy nuclei.

FIG. 7 and FIG. 8 show how the line shapes depend on the quadrupole asymmetry parameter η_(Q) and on the relative orientation θ_(QD), φ_(QD) of the internuclear nitrogen-carbon vector with respect to the principal axis system of the quadrupole tensor. It is possible to determine these parameters by analysis of the line-shapes. Indeed, the efficiency of the ¹⁴N single- or double-quantum excitation (and hence the line-shapes) depends on the magnitude of the quadrupole tensor and on its relative orientation with respect to the ¹³C-¹⁴N dipole-dipole interaction.

The samples were packed in 2.5 mm outer diameter ZrO₂ rotors (sample volume ca. 11 μl), and spun at 30 kHz in a Bruker triple resonance CP-MAS probe where one channel was adapted for nitrogen-14 resonance, using the 9.4 T wide-bore magnet (¹³C and ¹⁴N Larmor frequencies of 100.6 and 28.9 MHz) of an Avance 400 spectrometer. The magic angle was adjusted within 0.004°.^([38]) Cross-polarization (CP) was used with a constant proton RF amplitude ν_(RF) ^(H)=85 kHz while ν_(RF) ^(C) was ramped. Two-pulse phase-modulation (TPPM) proton decoupling was used during the entire experiment with an RF amplitude 100 kHz, pulse-widths of 3.9 μs, and a phase difference between two successive pulses of 35°. The RF amplitude of the ¹⁴N pulses was calibrated by direct detection of ¹⁴NH₄NO₃, which has a very small quadrupole splitting. The ¹⁴N pulses had an amplitude of ν_(RF) ^(N)=60 kHz using a 500 W amplifier. The samples of L-alanine (¹⁴NH₄ ⁺¹³C^(α)HCH₃COO⁻), glycine (¹⁴NH₄ ⁺¹³C^(α)H₂COO⁻), L-leucine (¹⁴NH₄ ⁺¹³C^(α)HRCOO⁻) with R=CH₂CH(CH₃)₂ and the tri-peptide L-ala-L-ala-gly, all enriched in the ¹³C^(α) positions, were purchased from Cambridge Isotope Laboratories, and used without further purification.

FIG. 1 shows pulse sequence and coherence transfer pathways for the excitation of ¹⁴N single- or double-quantum coherences in two-dimensional correlation experiments for solids rotating at the magic angle. The sequence starts with cross-polarization from protons to carbon-13 to generate C_(X) magnetization, followed by an interval τ_(exc)≈½D where the residual dipolar splitting D and the scalar coupling J between ¹⁴N and ¹³C lead to anti-phase coherences T^(C) ₁₁T^(N) ₁₀ and T^(C) ₁₁T^(N) ₂₀. In the ¹⁴N single-quantum experiment (SQ), these are converted into heteronuclear coherences T^(C) ₁₁T^(N) ₁₁ and T^(C) ₁₁T^(N) ₂₁ by applying an RF pulse of duration τ_(p) to the ¹⁴N nuclei, while in the ¹⁴N double-quantum experiment (DQ), one excites heteronuclear coherences T^(C) ₁₁T^(N) ₂₂. The evolution period t₁ is defined as the separation between the centers of the two RF pulses applied to the ¹⁴N nuclei, with a duration t₁=nt_(rot)(n=1, 2, . . . N). In this interval, the coherences evolve chiefly under the second-order quadrupole interaction, before being converted back into observable C_(X) magnetization. The coherence transfer pathway diagrams show that pure two-dimensional line shapes are obtained. The SQ experiment uses a simple phase alternation of the first ¹⁴N pulse with addition and subtraction of the ¹³C signals, while the DQ experiments requires a 4-step cycle of the phase of the first ¹⁴N pulse (0, 90, 180, 270°), again with addition and subtraction of the ¹³C signals. In addition, the first ¹H pulse may be phase-alternated, and the ¹³C π pulse may be exorcycled.

FIG. 2 shows simulations of ¹⁴N single-quantum (SQ) powder patterns that result from the pulse sequence of FIG. 1 for different excitation intervals τ_(exc) and ¹⁴N pulse lengths τ_(p). The radio-frequency (RF) field amplitude is ν_(RF)=60 kHz, the quadrupolar parameters are C_(Q)=1.2 MHz and η_(Q)=0.2, the dipolar interaction corresponds to a typical ¹⁴N-¹³C bond length (d_(CN)=667 Hz) leading to a residual dipolar splitting D≈25 Hz at 9.4 T. The powder pattern drawn with a thick line represents the ideal line-shape of the single-quantum ¹⁴N MAS spectrum obtained with ideal excitation and rotor synchronized acquisition.

FIG. 3 shows simulations of ¹⁴N double-quantum (DQ) powder patterns with the same parameters as in FIG. 2. The powder pattern drawn with a thick line represents the ideal line shape for the double-quantum ¹⁴N MAS spectrum obtained with ideal excitation and rotor synchronized acquisition.

FIG. 4 shows (a, b) experimental ¹³C CPMAS and two-dimensional ¹⁴N/¹³C correlation spectra showing isotropic ¹³C chemical shifts along the horizontal ω₂ axis (δ₂ labeled in ppm with respect to TMS) and ¹⁴N (c, d) single- and (e, f) double-quantum signals along the vertical ω₁ axis (δ₁ labeled in ppm with respect to ¹⁴NH₄NO₃). (a) In L-alanine (¹⁴NH₄ ⁺¹³C^(α)HCH₃COO⁻) the ¹³C CPMAS spectrum reveals an ill-resolved residual dipolar splitting (see expansion); (b) in glycine (¹⁴NH₄ ⁺¹³C^(α)H₂COO⁻) there is no visible residual dipolar splitting. Nevertheless, the ¹⁴ N single- and double-quantum coherences can be excited efficiently and the projections onto the δ₁ axis (g-j) reveal characteristic second-order quadrupolar powder patterns. For L-alanine C_(Q)≈1.2 MHz and η_(Q)≈0.3; for glycine C_(Q)≈1.2 MHz and η_(Q)≈0.5. Under our experimental conditions the T₂′(¹³C^(α)) values are found to be 28 and 23 ms for L-alanine and glycine, respectively. The CPMAS spectra (a, b) result from averaging 8 transients with relaxation intervals of 5 s. The two-dimensional spectra result from averaging (c, d) 32 and (e, f) 96 transients for each of (c, d) 512 and (e, f) 170 t₁ increments Δt₁=1/ν_(rot)=33.33 μs, with a relaxation interval of 3 s. The intervals τ_(exc)=τ_(rec) were 16 ms, while τ_(p) was (c, d) 11 μs and (e, f) 15 μs. The CP contact times for L-ala and gly were 0.5 and 1 ms, respectively.

FIG. 5 shows (a) experimental ¹³C CPMAS and two-dimensional ¹⁴N/¹³C correlation spectra obtained with (b) single- and (c) double-quantum methods of L-leucine that has two magnetically inequivalent sites I and II for ¹⁴N and ¹³C^(α). The projections onto the δ₁ axis (right) reveal second-order quadrupolar powder patterns that resembles simulated patterns with C_(Q) ^(I)≈1.2 MHz, C_(Q) ^(II)≈1.1 MHz, η_(Q) ^(I)≈0.3, and η_(Q) ^(II)≈0.1. The T₂′ values of the two ¹³C^(α) sites in L-leu are found to be (I) 26 and (II) 22 ms. The CPMAS spectrum (a) results from averaging 8 transients with a relaxation interval of 5 s. The two-dimensional spectra result from averaging (b) 32 and (c) 96 transients for each of (b) 400 and (c) 190 t₁ increments of Δ_(t) ₁=1/ν_(rot)=33.33 μs, with a relaxation interval of 3 s. The intervals τ_(exc)=τ_(rec) were 16 ms, while τ_(p) was (b) 11 μs and (c) 23 μs. The CP contact time was 0.6 ms.

FIG. 6 shows (a) experimental ¹³C CPMAS and two-dimensional ¹⁴N/¹³C correlation spectra obtained with (b) single- and (c) double-quantum methods for the tripeptide L-ala-L-ala-gly where all ¹³C^(α) are enriched. For the amide sites (I) and (III), ¹⁴N SQ and DQ signals can be observed (projections on the right) despite very large first-order quadrupole couplings (C_(Q) ^(I)≈C_(Q) ^(III)≈3 MHz) and very short T₂′(¹³C^(α))=14, 11 and 8 ms for sites I, II and III respectively. The projections of the NH₃ ⁺ group of the first L-alanine onto the δ₁ axis (d, e) reveal powder patterns that correspond to C_(Q) ^(II)≈1.3 MHz, and η_(Q) ^(II)≈0.3. The line widths of all three sites in the SQ spectrum are broadened, most probably by local molecular motions. The CPMAS spectrum (a) results from averaging 8 transients with a relaxation interval of 5 s. The two-dimensional spectra result from averaging (b) 4096 and (c) 8192 transients for each of (b) 16 and (c) 20 t₁ increments Δt₁=1ν_(rot)=33.33 μs, with a relaxation interval of 2.5 s. The intervals τ_(exc)=τ_(rec) were 6 ms, while τ_(p) was (b) 11 μs and (c) 24 μs. The CP contact time was 0.5 ms. The projections of the N-terminal ¹⁴N resonances onto δ₁ axis (d, e) were extracted from two-dimensional spectra recorded with (d) 64 (e) 96 t₁ increments each with (d) 128 and (e) 1024 transients.

FIG. 7 shows simulations of SQ and DQ ¹⁴N spectra for C_(Q)=1.2 MHz and η_(Q)=0, 0.5 and 1, appropriate for B₀=9.4 T, τ_(exc)=15 ms, ν_(RF) ^(N)=60 kHz, ν_(rot)=30 kHz, τ_(p)=10 μs for SQ and τ_(p)=20 μs for DQ. The powder patterns drawn with thick lines represent spectra assuming ideal single- or double-quantum excitation and rotor synchronized acquisition.

FIG. 8 shows simulations of SQ and DQ ¹⁴N spectra for C_(Q)=1.2 MHz and η=0.5, appropriate for B₀=9.4 T, τ_(exc)=15 ms, ν_(RF) ^(N)=60 kHz, ν_(rot)=30 kHz, τ_(p)=10 μs for SQ and τ_(p)=20 μs for DQ, as a function of the polar angles θ_(QD), φ_(QD) of the internuclear vector r(¹⁴N, ¹³C) with respect to the principal axis system of the quadrupole tensor. For larger values of θ_(QD), the sensitivity of the line shapes to φ_(QD) is more pronounced.

To summarize, we have shown that by transferring coherence between ¹⁴N and ¹³C in solid powdered samples, one can indirectly detect the single- or double-quantum transitions of ¹⁴N nuclei. Under fast magic-angle spinning, the spectra are determined predominantly by second-order quadrupole interactions. The orientation of the principal components of the quadrupole tensor can be readily rationalized in terms of electronic charge distributions. In many respects, quadrupole tensors are more straightforward to relate to the local environment than chemical shift tensors.^([42]) Quadrupole tensors can give direct insight into the electronic charge distribution in molecules. For example, the extent of “pyramidalisation” of nitrogen atoms in peptide bonds would be much easier to assess if one could determine nitrogen-14 quadrupole tensors instead of nitrogen-15 chemical shift tensors. Nitrogen-14 NMR could become an important tool for biology, chemistry and material science. The new method bears a close analogy to earlier work on the indirect detection of nitrogen-15 NMR,^([43]) which was originally published without a catchy name, but later dubbed Heteronuclear Single Quantum Correlation (HSQC).

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1. A method for obtaining a two-dimensional NMR (=nuclear magnetic resonance) spectrum of quadrupolar nuclei of ¹⁴N having spin l=1 using magic angle spinning (=MAS) of a solid powder sample and transfer of coherence from a neighboring nucleus with spin S=½ to single- or double-quantum transitions of said quadrupolar nuclei of ¹⁴N having spin l=1, wherein the detection of the spectrum occurs indirectly via the spin S=½ nuclei, wherein the transfer of coherence occurs through residual dipolar splittings, the method comprising the steps of: a) exciting the neighboring nucleus single quantum coherence; b) applying a delay of τ_(exc)=1/(2D), wherein D is a splitting between the quadrupolar nuclei of ¹⁴N and the nuclei with spin S=½ due to residual dipolar splittings, leading to antiphase coherence; c) applying a first ¹⁴N RF-pulse of duration τ_(p) the quadrupolar nuclei of ¹⁴N having spin l=1 for transferring anti-phase coherence into heteronuclear coherence; d) applying a π-RF-pulse to the neighboring nucleus with spin S=½ in a middle of an evolution interval t₁; e) applying a second ¹⁴N RF-pulse at t₁ of duration τ_(p) to the quadrupolar nuclei of ¹⁴N having spin l=1, wherein to is an interval between centers of the first and the second ¹⁴N pulses; and f) recording the signal of the neighboring nucleus with spin S=½ after a duration τ_(rec)=1/(2D) in t₂, wherein t₂ is the detection time interval.
 2. The method of claim 1, wherein step a) comprises cross polarization from protons.
 3. The method of claim 1, wherein the neighboring nucleus with spin S=½ is chosen from the group consisting of ¹³C, ³¹P, ¹⁵N, ²⁹Si, and ¹H.
 4. The method of claim 1, wherein steps a) to f) are repeated for N rotor-synchronized increments t₁=nΔt₁ with Δt₁=1 /ν_(rot) and n=1 , 2, 3 . . . N in a manner of two-dimensional spectroscopy, wherein ν_(rot) is a spinning frequency of the solid powder sample.
 5. The method of claim 4, wherein time domain signals S(t₁, t₂) are Fourier transformed with respect to t₁ to yield a spectrum of the quadrupolar nuclei of ¹⁴N having spin l=1 in an ω₁ domain and with respect to t₂ to yield a spectrum of the neighboring nucleus with S=½ in an ω₂ domainI.
 6. The method of claim 1, wherein (π/2)_(φ) pulses are applied to the neighboring nucleus with S=½ at a beginning and at an end of the evolution interval t₁.
 7. The method of claim 1, wherein a z-filter is used before a detection period.
 8. The method of claim 1, wherein a quadrupolar coupling constant C_(Q), an asymmetry parameter η_(Q) of the quadrupolar nuclei of ¹⁴N having spin l=1, and a relative orientation of the quadrupolar tensor with respect to a bond between the quadrupolar nuclei of ¹⁴N having spin l=1 and the neighboring nucleus with S=½ are extracted from the obtained NMR spectra. 